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\(1.6x\left(x-10\right)-2x+20=0\)
⇔\(6x\left(x-10\right)-2\left(x-10\right)=0\)
⇔ \(2\left(x-10\right)\left(3x-1\right)=0\)
⇔ x = 10 hoặc x = \(\dfrac{1}{3}\)
KL....
\(2.3x^2\left(x-3\right)+3\left(3-x\right)=0\)
⇔ \(3\left(x-3\right)\left(x^2-1\right)=0\)
⇔ \(x=+-1\) hoặc \(x=3\)
KL....
\(3.x^2-8x+16=2\left(x-4\right)\)
⇔ \(\left(x-4\right)^2-2\left(x-4\right)=0\)
⇔ \(\left(x-4\right)\left(x-6\right)=0\)
⇔ \(x=4\) hoặc \(x=6\)
KL.....
\(4.x^2-16+7x\left(x+4\right)=0\)
\(\text{⇔}4\left(x+4\right)\left(2x-1\right)=0\)
⇔ \(x=-4hoacx=\dfrac{1}{2}\)
KL.....
\(5.x^2-13x-14=0\)
⇔ \(x^2+x-14x-14=0\)
\(\text{⇔}\left(x+1\right)\left(x-14\right)=0\)
\(\text{⇔}x=14hoacx=-1\)
KL......
Còn lại tương tự ( dài quá ~ )
a) \(x^4-10x^3+25x^2=0\)
\(\Leftrightarrow x^2\left(x^2-10x+25\right)=0\)
\(\Leftrightarrow x^2\left(x-5\right)^2=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x^2=0\\\left(x-5\right)^2=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=5\end{array}\right.\)
b) \(x^3+3x^2+3x+1=0\)
\(\Leftrightarrow\left(x+1\right)^3=0\)
\(\Leftrightarrow x+1=0\)
\(\Leftrightarrow x=-1\)
a) x4 - 10x3 + 25x2 = (x2)2 - 2.x2.5x + (5x)2 = (x2 - 5x)2 = 0 => x(x - 5) = 0 => x = 0 hay x - 5 = 0 => x = 0 ; 5
b) x3 + 3x2 + 3x + 1 = x3 + 3.x2.1 + 3.x.12 + 13 = (x + 1)3 = 0 => x + 1 = 0 => x = -1
a,x^2(x^2-10x+25)=0
x^2(x-5)^2=0
=> x^2=0 hoac (x-5)^2=0
=>x=0 hoac 5
a) 5x ( x - 2000 ) - x + 2000 = 0
5x ( x - 2000 ) - ( x - 2000 ) = 0
5x ( x - 2000 ) = 0
\(\Rightarrow\orbr{\begin{cases}5x=0\\x-2000=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=2000\end{cases}}\)
Vậy ....
b) x3 - 13x = 0
x ( x2 - 13 ) = 0
x ( x - \(\sqrt{13}\)) - ( x + \(\sqrt{13}\)) = 0
\(\Rightarrow\hept{\begin{cases}x=0\\x-\sqrt{13}\\x+\sqrt{13}\end{cases}}\Rightarrow\hept{\begin{cases}x=0\\x=\sqrt{13}\\x=\sqrt{-13}\end{cases}}\)
Vậy ....
a) x2 + 6 + 9
= x2 + 2 . 3 . x + 32
= ( x + 3 )2
b) 10x - 25 - x2
= - ( x2 - 10x + 25 )
= - ( x - 5 )2
c) 8x3 - 1/8
= ( 2x )3 - ( 1/2 )3
= ( 2x - 1/2 ) ( 4x2 + x + 1/4 )
d) 1/25 x2 - 64x2
= ( 1/5x )2 - ( 8x )2
= ( 1/5x + 8x ) ( 1/5 - 8x )
\(x^3-13x=0\)
<=> \(x\left(x^2-13\right)=0\)
<=> \(x\left(x-\sqrt{13}\right)\left(x+\sqrt{13}\right)=0\)
<=> \(x=0\)
hoặc \(x-\sqrt{13}=0\)
hoặc \(x+\sqrt{13}=0\)
<=> .....
a) 2x(x - 3) + 5(x - 3) = 0 ⇔ (x - 3)(2x + 5) = 0 ⇔ x - 3 = 0 hoặc 2x + 5 = 0
1) x - 3 = 0 ⇔ x = 3
2) 2x + 5 = 0 ⇔ 2x = -5 ⇔ x = -2,5
Vậy tập nghiệm của phương trình là S = {3;-2,5}
b) (x2 - 4) + (x - 2)(3 - 2x) = 0 ⇔ (x - 2)(x + 2) + (x - 2)(3 - 2x) = 0
⇔ (x - 2)(x + 2 + 3 - 2x) = 0 ⇔ (x - 2)(-x + 5) = 0 ⇔ x - 2 = 0 hoặc -x + 5 = 0
1) x - 2 = 0 ⇔ x = 2
2) -x + 5 = 0 ⇔ x = 5
Vậy tập nghiệm của phương trình là S = {2;5}
c) x3 – 3x2 + 3x – 1 = 0 ⇔ (x – 1)3 = 0 ⇔ x = 1.
Vậy tập nghiệm của phương trình là x = 1
d) x(2x - 7) - 4x + 14 = 0 ⇔ x(2x - 7) - 2(2x - 7) = 0
⇔ (x - 2)(2x - 7) = 0 ⇔ x - 2 = 0 hoặc 2x - 7 = 0
1) x - 2 = 0 ⇔ x = 2
2) 2x - 7 = 0 ⇔ 2x = 7 ⇔ x = 72
Vậy tập nghiệm của phương trình là S = {2;72}
e) (2x – 5)2 – (x + 2)2 = 0 ⇔ (2x - 5 - x - 2)(2x - 5 + x + 2) = 0
⇔ (x - 7)(3x - 3) = 0 ⇔ x - 7 = 0 hoặc 3x - 3 = 0
1) x - 7 = 0 ⇔ x = 7
2) 3x - 3 = 0 ⇔ 3x = 3 ⇔ x = 1
Vậy tập nghiệm phương trình là: S= { 7; 1}
f) x2 – x – (3x - 3) = 0 ⇔ x2 – x – 3x + 3 = 0
⇔ x(x - 1) - 3(x - 1) = 0 ⇔ (x - 3)(x - 1) = 0
⇔ x = 3 hoặc x = 1
Vậy tập nghiệm của phương trình là S = {1;3}
a) ( x - 1 )2 - ( x - 1 )( x + 1 ) = 0
<=> x2 - 2x + 1 - ( x2 - 1 ) = 0
<=> x2 - 2x + 1 - x2 + 1 = 0
<=> 2 - 2x = 0
<=> 2x = 2
<=> x = 1
b) ( 2x - 1 )2 - ( 2x + 1 )2 = 0
<=> [ ( 2x - 1 ) - ( 2x + 1 ) ][ ( 2x - 1 ) + ( 2x + 1 ) ] = 0
<=> ( 2x - 1 - 2x - 1 )( 2x - 1 + 2x + 1 ) = 0
<=> -2.4x = 0
<=> -8x = 0
<=> x = 0
c) 25( x + 3 )2 + ( 1 - 5x )( 1 + 5x ) = 8
<=> 52( x + 3 )2 + 12 - 25x2 = 8
<=> [ 5( x + 3 ) ]2 + 1 - 25x2 = 8
<=> ( 5x + 15 )2 + 1 - 25x2 = 8
<=> 25x2 + 150x + 225 + 1 - 25x2 = 8
<=> 150x + 226 = 8
<=> 150x = -218
<=> x = -218/150 = -109/75
d) 9( x + 1 )2 - ( 3x - 2 )( 3x + 2 ) = 10
<=> 32( x + 1 )2 - ( 9x2 - 4 ) = 10
<=> [ 3( x + 1 ) ]2 - 9x2 + 4 = 10
<=> ( 3x + 3 )2 - 9x2 + 4 = 10
<=> 9x2 + 18x + 9 - 9x2 + 4 = 10
<=> 18x + 13 = 10
<=> 18x = -3
<=> x = -3/18 = -1/6
a) (x - 1)2 - (x - 1)(x + 1) = 0
=> (x - 1)2 - (x2 - 12) = 0
=> x2 - 2.x.1 + 12 - x2 + 1 = 0
=> x2 - 2x + 1 - x2 + 1 = 0
=> -2x + 1 + 1 = 0
=> -2x + 2 = 0
=> -2x = -2 => x = 1
b) (2x - 1)2 - (2x + 1)2 = 0
=> (2x - 1 - 2x + 1)(2x - 1 + 2x + 1) = 0
=> 0 = 0(đúng)
c) 25(x + 3)2 + (1 - 5x)(1 + 5x) = 8
=> 25(x2 + 2.x.3 + 32) + (12 - (5x)2) = 8
=> 25x2 + 150x + 225 + 1 - 25x2 = 8
=> 150x +225 + 1 = 8
=> 150x = -218
=> x = -109/75
d) 9(x + 1)2 - (3x - 2)(3x + 2) = 10
=> 9(x2 + 2x + 1) - [(3x)2 - 22 ] = 10
=> 9x2 + 18x + 9 - (9x2 - 4) = 10
=> 9x2 + 18x + 9 - 9x2 + 4 = 10
=> 18x + 9 + 4 = 10
=> 18x = -3
=> x = -1/6
Tìm x
a) 9(3x-2)=x(2-3x)
b) 25x2-2=0
c) x2-25=6x-9
d) (x+2)2-(x-2)(x+2)=0
e) x3-8=(x-2)3
f) x3+5x2-4x-20=0
a) 9(3x - 2) = x(2 - 3x)
\(\Leftrightarrow\)-9(2 - 3x) = x(2 - 3x)
\(\Leftrightarrow\)-9(2 - 3x) - x(2 - 3x) = 0
\(\Leftrightarrow\)(2 - 3x)(- 9 - x) = 0
\(\Leftrightarrow\)2 - 3x = 0 hay - 9 - x = 0
\(\Leftrightarrow\) 3x = 2 \(\Leftrightarrow\) x = - 9
\(\Leftrightarrow\) x = 2/3
b) 25x2 - 2 = 0
\(\Leftrightarrow\)(5x)2 - (\(\sqrt{2}\))2 = 0
\(\Leftrightarrow\)(5x - \(\sqrt{2}\))(5x + \(\sqrt{2}\)) = 0
\(\Leftrightarrow\)5x - \(\sqrt{2}\)= 0 hay 5x + \(\sqrt{2}\)= 0
\(\Leftrightarrow\)5x = \(\sqrt{2}\) \(\Leftrightarrow\)5x = -\(\sqrt{2}\)
\(\Leftrightarrow\) x = \(\sqrt{2}\)/5 \(\Leftrightarrow\) x = -\(\sqrt{2}\)/5
c) x2 - 25 = 6x - 9
\(\Leftrightarrow\)(x2 - 6x + 9) - 25 = 0
\(\Leftrightarrow\)(x - 3)2 - 52 = 0
\(\Leftrightarrow\)(x - 3 - 5)(x - 3 + 5) = 0
\(\Leftrightarrow\)(x - 7)(x + 2) = 0
\(\Leftrightarrow\)x - 7 = 0 hay x + 2 = 0
\(\Leftrightarrow\)x = 7 \(\Leftrightarrow\)x = -2
d) (x + 2)2 - (x - 2)(x + 2) = 0
\(\Leftrightarrow\)(x + 2)(x + 2) - (x - 2)(x + 2) = 0
\(\Leftrightarrow\)(x + 2)(x + 2 - x + 2) = 0
\(\Leftrightarrow\)(x + 2)4 = 0 (hay 4(x + 2) = 0)
\(\Leftrightarrow\)x + 2 = 0 (vì 4 \(\ne\)0)
\(\Leftrightarrow\)x = -2
e) x3 - 8 = (x - 2)3
\(\Leftrightarrow\)x3 - 23 = (x - 2)3
\(\Leftrightarrow\)(x - 2)(x2 + 2x + 4) = (x - 2)3
\(\Leftrightarrow\)(x - 2)(x2 + 2x + 4) - (x - 2)3 = 0
\(\Leftrightarrow\)(x - 2)(x2 + 2x + 4) - (x - 2)(x - 2)2 = 0
\(\Leftrightarrow\)(x - 2)[x2 + 2x + 4 - (x - 2)2] = 0
\(\Leftrightarrow\)(x - 2)[x2 + 2x + 4 - (x2 - 4x + 4)] = 0
\(\Leftrightarrow\)(x - 2)(x2 + 2x + 4 - x2 + 4x - 4) = 0
\(\Leftrightarrow\)(x - 2)6x = 0 (hay 6x(x - 2) = 0)
\(\Leftrightarrow\)x - 2 = 0 hay x = 0 (vì 6\(\ne\)0)
\(\Leftrightarrow\)x = 2
f) x3 + 5x2 - 4x - 20 = 0
\(\Leftrightarrow\)x2(x + 5) - 4(x + 5) = 0
\(\Leftrightarrow\)(x + 5)(x2 - 4) = 0
\(\Leftrightarrow\)(x + 5)(x - 2)(x + 2) = 0
\(\Leftrightarrow\)x + 5 = 0 hay x - 2 = 0 hay x + 2 = 0
\(\Leftrightarrow\)x = -5 \(\Leftrightarrow\)x = 2 \(\Leftrightarrow\)x = -2
a) \(\left(y-1\right)^2=9\)
\(\Rightarrow\left(y-1\right)^2=3^2=\left(-3\right)^2\)
\(\Rightarrow x-1=3\Rightarrow x=4\)
\(\Rightarrow x-1=-3\Rightarrow x=-2\)
Vậy: \(x=4\) hoặc \(-2\)
a) \(\left(x^2-1\right)\left(x^2-25\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2-1=0\\x^2-25=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x^2=1\\x^2=25\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\pm1\\x=\pm5\end{cases}}\)
b) \(x^2-8x+16=0\)
\(\Leftrightarrow\left(x-4\right)^2=0\)
\(\Leftrightarrow x-4=0\)
\(\Leftrightarrow x=4\)
c) \(x^3+3x^2+3x+1=0\)
\(\Leftrightarrow\left(x+1\right)^3=0\)
\(\Leftrightarrow x+1=0\)
\(\Rightarrow x=-1\)
d) \(x^3+10x^2+25x=0\)
\(\Leftrightarrow x\left(x+5\right)^2=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)
a) ( x2 - 1 )( x2 - 25 ) = 0
<=> \(\orbr{\begin{cases}x^2-1=0\\x^2-25=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\pm1\\x=\pm5\end{cases}}\)
b) x2 - 8x + 16 = 0
<=> ( x - 4 )2 = 0
<=> x - 4 = 0
<=> x = 4
c) x3 + 3x2 + 3x + 1 = 0
<=> ( x + 1 )3 = 0
<=> x + 1 = 0
<=> x = -1
d) x3 + 10x2 + 25x = 0
<=> x( x2 + 10x + 25 ) = 0
<=> x( x + 5 )2 = 0
<=> \(\orbr{\begin{cases}x=0\\x+5=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)